In this work, we present EAGr, a system for supporting large numbers of continuous neighborhood-based ("ego-centric") aggregate queries over large, highly dynamic, and rapidly evolving graphs. Examples of such queries include computation of personalized, tailored trends in social networks, anomaly/event detection in financial transaction networks, local search and alerts in spatio-temporal networks, to name a few. Key challenges in supporting such continuous queries include high update rates typically seen in these situations, large numbers of queries that need to be executed simultaneously, and stringent low latency requirements. We propose a flexible, general, and extensible in-memory framework for executing different types of ego-centric aggregate queries over large dynamic graphs with low latencies. Our framework is built around the notion of an aggregation overlay graph, a pre-compiled data structure that encodes the computations to be performed when an update/query is received. The overlay graph enables sharing of partial aggregates across multiple ego-centric queries (corresponding to the nodes in the graph), and also allows partial pre-computation of the aggregates to minimize the query latencies. We present several highly scalable techniques for constructing an overlay graph given an aggregation function, and also design incremental algorithms for handling structural changes to the underlying graph. We also present an optimal, polynomial-time algorithm for making the pre-computation decisions given an overlay graph, and evaluate an approach to incrementally adapt those decisions as the workload changes. Although our approach is naturally parallelizable, we focus on a single-machine deployment and show that our techniques can easily handle graphs of size up to 320 million nodes and edges, and achieve update/query throughputs of over 500K/s using a single, powerful machine.